Aptitude Discussion

Q. |
On May 1, 2007, two organisations ($A$ and $B$) were formed with $n$ members each. On the first day of each subsequent month, $m$ members join $A$ while the number of members in $B$ gets multiplied by $p$. On September 2, 2007, both organisations have the same number of members. If $m = 20n$, find $p$? |

✖ A. |
2 |

✔ B. |
3 |

✖ C. |
4 |

✖ D. |
5 |

**Solution:**

Option(**B**) is correct

The number of members in $A$ on Oct 2, 2007:

$=n+4m=n+80n=81n$

Number of members in $B$ on Oct 2, 2007:

$=n×p×p×p×p$

As given in the question, now both organisations have the same number of members.

$⇒ 81n=n×p^4$

$⇒ p=3$

Note: As per the comment by **Prabal** the date mentioned in the *question *has been **changed to September 2** from October 2.

**Prabal**

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Thank you Prabal for pointing out the correction. Updated the question.

**Anurag**

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Mistake in Question .. Guys .. Has to be Sep 2007 instead f Oct 2007 ..

**Pranshu**

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it must be $n+5m=np^5$

From May to October is 6 months, therefore the problem entails 6 terms of both series,

thus, the equation shall be $n+5m=np^5$, which shall obviously not give a valid answer. Thus, the date should be September 2nd not October 2nd.